User talk:F2dk
Welcome Hi, welcome to Mancala World! Thanks for your edit to the File:Kalahresults.png page. Please leave a message on my talk page if I can help with anything! -- Mr Mancala (Talk) 10:41, April 14, 2011 Congratulations for solving (6;6) Kalah! You wrote: "If all pits on your side become empty, the opponent captures all of the remaining stones in his pits." This is only correct, if it is your turn. Otherwise the opponent may sow to your side and the game continues. BTW, what happens if you play with the pie rule?--Mr Mancala 13:13, April 15, 2011 (UTC) :::First of all, thank you for your interest and feedback! :::I have used the rules given in J. Donkers' article Solving Kalah from 2000. He used the rule that says: "The game ends whenever a move leaves no counters on one player’s side, in which case the other player captures all remaining counters". This means that when one side becomes empty, the stones on the other side are captured, and the game ends immediately. You can confirm this yourself by looking at the table of Game-theoretic values for pits=1 and stones-per-pit=5 (with your rule it would end in a draw, but Donkers showed it ends in a win -- see this illustration). :::Since my main goal was to fill out the (6,6) square in J. Donkers' article, I have used the same rules as him. However I am also interested in solving different variants of Kalaha, so I have taken note of your variant and I might solve it in the future. Thank you for making me aware of this rule. :::Regarding the pie rule, I am not sure how it is used in Kalaha. Maybe you can elaborate how exactly it is used in practice? Give an example of how a game could start when the pie rule is used. :::Maybe this helps answer your question: To win, the first player doesn't have to start by taking an extra turn. You can see this when playing against my computer (unless you are using Safari). :::--F2dk 16:26, April 15, 2011 (UTC) :Thank you very much for your reply. I re-read the patent issued by Champion and found that you were indeed correct - in fact, according to the original rules, a game of Kalah ends, when one player no longer has any seeds in any of his holes. In many traditional games (this includes many famous ones; e.g. Oware and Congkak) a game ends, when a player who is to play has no legal move, which might have been the reason for my mistake. I changed the rules description on this site. Thank you. The pie rule was implemented at igGameCenter and Vying and maybe a few more sites. Playing 1 (the move which results in a bonus move in (6;6)-Kalah) is considered a loosing-move, because the opponent would switch sides. Do you know if starting with another hole would result in a draw if the players continue to play perfectly afterwards? This would be very interesting for expert players! ----Mr Mancala 12:55, April 22, 2011 (UTC) :::Hi, Mr Mancala. Sorry for not seeing your reply - better late than never, right? :) I know that for all 4 variations of kalaha I have investigated, you can force a win with other starting moves than 1. But does a move exist that can guarantee only a draw? I will cite my thesis from 2011: :::::In kalaha, some players play with the pie rule. It means that the starting player makes the ﬁrst move, and then the second player decides if he wants to take the ﬁrst player’s seat. This rule forces the ﬁrst player to make a weaker ﬁrst move than he normally would. Optimally the ﬁrst player should choose a move that always leads to a draw. That way, regardless of whether the pie rule comes into play, the starting player has at least secured himself a draw. But does such a move exist? Our initial ﬁnding say yes, but we have not conﬁrmed it yet. :::Unfortunately I never gotten around to actually confirm it. :::By the way, my reference implementation of the perfect kalaha player always starts by playing 2. I only did this because I thought it would be a more impressive way to win. ;) :::--F2dk (talk) 07:09, April 11, 2016 (UTC) ---- Hi Anders- I'm Mark Rawlings and I've been working on Kalah for many years. I was able to quantify the results of each of the first moves for the "empty capture" variant of Kalah(6,6), and also prove that the "standard variant" of Kalah(6,6) is at least a win by 4. I had added the "Computer Analysis" section for the Wikipedia entry on Kalah (en.wikipedia.org/wiki/Kalah). I believe your results could add some missing information on the standard version of Kalah(6,6). Have you analysed each of the 10 first moves in the standard variant? (I have two proven wins and two proven losses so far.) That would be good information to have! I'm hoping to buy or build a computer with 64 GB of ram soon (been putting it off for about a year), which would allow me to create the 35 and 36-seed endgame databeses and quantify the magnitude of the wins/losses for the standard variant of 6,6. Regards, - Mark 21:01, November 16, 2016 (UTC)MarkR27 (talk) :::Hi, Mark. ::: :::Congratulations on your results so far. I find it exciting that we are still uncovering new knowledge about this great game. :::When you say "standard variant", I interpret it like this: :::*If your sowing ends up in an empty pit on your own side, you capture both your own seed and the opposite pit's seeds IF the opposite pit is not empty :::*If all 6 pits on one side of the board becomes empty, the other player captures all of the stones in his 6 pits :::Back in 2011, I did not analyze all 10 openings for this variant. But since you thought it would be helpful, I fired up my analysis program once again. It ran for about 24 hours, and the results are now in: :::The openings 1-2, 1-3 and 2 are the only winning moves. I cannot say which of the remaining moves are ties and losses, since my program does not distinguish between that. :::The opening 3 was very close to a win, though. Responding with 2, 4, 5, 6 all end up with a win for the starting player. But playing 3 counters it. (Move 1 was unanalyzed.) :::Let me know if there is anything else I can help with. :::--F2dk (talk) 10:56, November 19, 2016 (UTC) Hi Anders- Great to hear from you! Yes, your description of "standard variant" is the same as mine. Thanks for running the rest of the opening moves. Your results are consistent with mine. I also proved that 1-2 and 1-3 are wins, with 1-3 being a win by at least 4. (Move 2 was trending towards a win, but I wasn't able to prove it with my current computer configuration.) I was also able to prove that moves 1-6 and 6 are losses. I ran a deep search on the other moves, including move 3, and they are all probable draws based on deep searches. (I wasn't able to search the entire game tree, though, so the draws aren't proven.) Question about your perfect solver on-line: Can it be revised so the other side can start the game, or for other starting moves? Have a good day! - Mark MarkR27 (talk) 00:00, November 21, 2016 (UTC) :::Hi Mark :::That's good to hear! :::My online perfect player can only play the winning player, so it must start. :::I could add more openings but it takes a long time to compute the opening book, so I'd rather not. Why is that interesting to you anyway, if I may ask? :::--F2dk (talk) 18:38, November 23, 2016 (UTC) :::Hi Anders- :::No problem. I was just going to play around with it and maybe verify some of my results. I looked at the opening move 3 with a response of 1, and it is a win by at least 4 for the first player. (I prove a win by 2 in about 2 hours and a win by 4 in about 6 hours. Still running...) Since I can't do much more with my current computer configuration, I was thinking of modifying my program to just look for wins (like yours). Should be a lot faster! :::MarkR27 (talk) 21:08, November 23, 2016 (UTC)